The Convolution Property
Reference: Logan, A First Course in Differential Equations, 3rd ed., §3.3 "The Convolution Property", pp. 160-163
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §3.3 “The Convolution Property”, pp. 160-163 |
| Read this week | Week 8 of the quarter: pages 160 to 163 |
Bring your copy of Logan to this topic. The section and pages above are the exact reading for this skill.
Objectives
By the end of this section you should be able to:
- Define the convolution of two functions as an integral
- State and use the convolution property, that the transform of a convolution is a product
- Invert a product of transforms as a convolution integral
- Solve a forced equation by writing its particular solution as a convolution
Prerequisite Check
Before this section, make sure you are comfortable with:
- Solving initial value problems with the Laplace transform
- Integrating products of exponentials, sines, and cosines
Status
A guided stub for now. You get the exact Logan reading with page numbers, the week it falls in the quarter, the learning targets, and what to review first. The full worked examples and the leveled practice set for this section are being written and will appear here.